On the Rankin-Selberg problem

被引：52

作者：

Huang, Bingrong ^{[1
,2
]}

机构：

[1] Shandong Univ, Data Sci Inst, Jinan 250100, Shandong, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

MATHEMATISCHE ANNALEN | 2021年 / 381卷 / 3-4期

关键词：

SUBCONVEXITY; SUMMATION;

D O I：

10.1007/s00208-021-02186-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we solve the Rankin-Selberg problem. That is, we break the well known Rankin-Selberg's bound on the error term of the second moment of Fourier coefficients of a GL(2) cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.

引用

页码：1217 / 1251

页数：35

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